LMFDB - Embedded newform 370.2.b.d.149.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [370,2,Mod(149,370)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("370.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(370, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,-10,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.12837029094400.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 51x^{6} - 124x^{5} + 154x^{4} - 46x^{3} + x^{2} + 4x + 8 $ x^10 - 2x^9 + 2x^8 - 4x^7 + 51x^6 - 124x^5 + 154x^4 - 46x^3 + x^2 + 4x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.3
Root			$0.478560 - 0.478560i$ of defining polynomial
Character	$\chi$	$=$	370.149
Dual form			370.2.b.d.149.8

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -0.332924i q^{3} -1.00000 q^{4} +(-1.10390 + 1.94458i) q^{5} -0.332924 q^{6} -3.51336i q^{7} +1.00000i q^{8} +2.88916 q^{9} +(1.94458 + 1.10390i) q^{10} -0.290044 q^{11} +0.332924i q^{12} -7.12558i q^{13} -3.51336 q^{14} +(0.647398 + 0.367517i) q^{15} +1.00000 q^{16} -6.17921i q^{17} -2.88916i q^{18} -5.83553 q^{19} +(1.10390 - 1.94458i) q^{20} -1.16968 q^{21} +0.290044i q^{22} +6.45973i q^{23} +0.332924 q^{24} +(-2.56279 - 4.29326i) q^{25} -7.12558 q^{26} -1.96065i q^{27} +3.51336i q^{28} +1.18043 q^{29} +(0.367517 - 0.647398i) q^{30} +9.77838 q^{31} -1.00000i q^{32} +0.0965628i q^{33} -6.17921 q^{34} +(6.83201 + 3.87841i) q^{35} -2.88916 q^{36} -1.00000i q^{37} +5.83553i q^{38} -2.37228 q^{39} +(-1.94458 - 1.10390i) q^{40} +1.64077 q^{41} +1.16968i q^{42} +5.34889i q^{43} +0.290044 q^{44} +(-3.18936 + 5.61821i) q^{45} +6.45973 q^{46} +5.69256i q^{47} -0.332924i q^{48} -5.34367 q^{49} +(-4.29326 + 2.56279i) q^{50} -2.05721 q^{51} +7.12558i q^{52} -9.32034i q^{53} -1.96065 q^{54} +(0.320181 - 0.564014i) q^{55} +3.51336 q^{56} +1.94279i q^{57} -1.18043i q^{58} -5.94279 q^{59} +(-0.647398 - 0.367517i) q^{60} -1.27699 q^{61} -9.77838i q^{62} -10.1507i q^{63} -1.00000 q^{64} +(13.8563 + 7.86596i) q^{65} +0.0965628 q^{66} +6.04334i q^{67} +6.17921i q^{68} +2.15060 q^{69} +(3.87841 - 6.83201i) q^{70} +13.4995 q^{71} +2.88916i q^{72} -1.71348i q^{73} -1.00000 q^{74} +(-1.42933 + 0.853215i) q^{75} +5.83553 q^{76} +1.01903i q^{77} +2.37228i q^{78} -8.25422 q^{79} +(-1.10390 + 1.94458i) q^{80} +8.01474 q^{81} -1.64077i q^{82} -2.41807i q^{83} +1.16968 q^{84} +(12.0160 + 6.82126i) q^{85} +5.34889 q^{86} -0.392995i q^{87} -0.290044i q^{88} +10.2797 q^{89} +(5.61821 + 3.18936i) q^{90} -25.0347 q^{91} -6.45973i q^{92} -3.25546i q^{93} +5.69256 q^{94} +(6.44187 - 11.3477i) q^{95} -0.332924 q^{96} +15.1272i q^{97} +5.34367i q^{98} -0.837984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{4} + 6 q^{5} - 6 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{14} + 10 q^{16} - 8 q^{19} - 6 q^{20} + 32 q^{21} + 4 q^{25} - 12 q^{26} - 22 q^{29} + 20 q^{30} + 46 q^{31} - 18 q^{34} + 32 q^{35} + 6 q^{36}+ \cdots + 22 q^{99}+O(q^{100}) $ 10 * q - 10 * q^4 + 6 * q^5 - 6 * q^9 + 2 * q^10 + 6 * q^11 + 2 * q^14 + 10 * q^16 - 8 * q^19 - 6 * q^20 + 32 * q^21 + 4 * q^25 - 12 * q^26 - 22 * q^29 + 20 * q^30 + 46 * q^31 - 18 * q^34 + 32 * q^35 + 6 * q^36 - 40 * q^39 - 2 * q^40 - 14 * q^41 - 6 * q^44 + 2 * q^45 + 12 * q^46 - 60 * q^49 + 8 * q^50 - 40 * q^51 + 42 * q^55 - 2 * q^56 - 40 * q^59 - 18 * q^61 - 10 * q^64 + 4 * q^65 + 40 * q^66 - 32 * q^69 - 6 * q^70 + 12 * q^71 - 10 * q^74 + 50 * q^75 + 8 * q^76 - 40 * q^79 + 6 * q^80 - 14 * q^81 - 32 * q^84 + 36 * q^85 - 34 * q^86 - 24 * q^89 + 44 * q^90 + 32 * q^91 - 24 * q^94 + 12 * q^95 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	0.332924i		−	0.192214i	−0.995371	−	0.0961070i	$-0.969361\pi$
$3$		−	0.332924i		−	0.192214i	0.995371	−	0.0961070i	$-0.0306391\pi$
$4$	−1.00000			−0.500000
$5$	−1.10390	+	1.94458i	−0.493681	+	0.869643i
$5$	−1.10390	+	1.94458i	−0.493681	+	0.869643i
$6$	−0.332924			−0.135916
$7$		−	3.51336i		−	1.32792i	−0.747766	−	0.663962i	$-0.768874\pi$
$7$		−	3.51336i		−	1.32792i	0.747766	−	0.663962i	$-0.231126\pi$
$8$			1.00000i			0.353553i
$9$	2.88916			0.963054
$10$	1.94458	+	1.10390i	0.614930	+	0.349085i
$11$	−0.290044			−0.0874516			−0.0437258	−	0.999044i	$-0.513923\pi$
$11$	−0.290044			−0.0874516			−0.0437258	+	0.999044i	$0.513923\pi$
$12$			0.332924i			0.0961070i
$13$		−	7.12558i		−	1.97628i	−0.153559	−	0.988140i	$-0.549073\pi$
$13$		−	7.12558i		−	1.97628i	0.153559	−	0.988140i	$-0.450927\pi$
$14$	−3.51336			−0.938984
$15$	0.647398	+	0.367517i	0.167158	+	0.0948925i
$16$	1.00000			0.250000
$17$		−	6.17921i		−	1.49868i	−0.662187	−	0.749339i	$-0.730372\pi$
$17$		−	6.17921i		−	1.49868i	0.662187	−	0.749339i	$-0.269628\pi$
$18$		−	2.88916i		−	0.680982i
$19$	−5.83553			−1.33876			−0.669381	−	0.742919i	$-0.733441\pi$
$19$	−5.83553			−1.33876			−0.669381	+	0.742919i	$0.733441\pi$
$20$	1.10390	−	1.94458i	0.246841	−	0.434821i
$21$	−1.16968			−0.255246
$22$			0.290044i			0.0618376i
$23$			6.45973i			1.34695i	0.739212	+	0.673473i	$0.235198\pi$
$23$			6.45973i			1.34695i	−0.739212	+	0.673473i	$0.764802\pi$
$24$	0.332924			0.0679579
$25$	−2.56279	−	4.29326i	−0.512558	−	0.858653i
$26$	−7.12558			−1.39744
$27$		−	1.96065i		−	0.377326i
$28$			3.51336i			0.663962i
$29$	1.18043			0.219201			0.109600	−	0.993976i	$-0.465043\pi$
$29$	1.18043			0.219201			0.109600	+	0.993976i	$0.465043\pi$
$30$	0.367517	−	0.647398i	0.0670991	−	0.118198i
$31$	9.77838			1.75625			0.878124	−	0.478433i	$-0.158795\pi$
$31$	9.77838			1.75625			0.878124	+	0.478433i	$0.158795\pi$
$32$		−	1.00000i		−	0.176777i
$33$			0.0965628i			0.0168094i
$34$	−6.17921			−1.05972
$35$	6.83201	+	3.87841i	1.15482	+	0.655571i
$36$	−2.88916			−0.481527
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$			5.83553i			0.946648i
$39$	−2.37228			−0.379869
$40$	−1.94458	−	1.10390i	−0.307465	−	0.174543i
$41$	1.64077			0.256245			0.128123	−	0.991758i	$-0.459105\pi$
$41$	1.64077			0.256245			0.128123	+	0.991758i	$0.459105\pi$
$42$			1.16968i			0.180486i
$43$			5.34889i			0.815698i	0.913049	+	0.407849i	$0.133721\pi$
$43$			5.34889i			0.815698i	−0.913049	+	0.407849i	$0.866279\pi$
$44$	0.290044			0.0437258
$45$	−3.18936	+	5.61821i	−0.475442	+	0.837513i
$46$	6.45973			0.952435
$47$			5.69256i			0.830346i	0.909743	+	0.415173i	$0.136279\pi$
$47$			5.69256i			0.830346i	−0.909743	+	0.415173i	$0.863721\pi$
$48$		−	0.332924i		−	0.0480535i
$49$	−5.34367			−0.763382
$50$	−4.29326	+	2.56279i	−0.607159	+	0.362433i
$51$	−2.05721			−0.288067
$52$			7.12558i			0.988140i
$53$		−	9.32034i		−	1.28025i	−0.768272	−	0.640123i	$-0.778883\pi$
$53$		−	9.32034i		−	1.28025i	0.768272	−	0.640123i	$-0.221117\pi$
$54$	−1.96065			−0.266810
$55$	0.320181	−	0.564014i	0.0431732	−	0.0760517i
$56$	3.51336			0.469492
$57$			1.94279i			0.257329i
$58$		−	1.18043i		−	0.154998i
$59$	−5.94279			−0.773686			−0.386843	−	0.922146i	$-0.626434\pi$
$59$	−5.94279			−0.773686			−0.386843	+	0.922146i	$0.626434\pi$
$60$	−0.647398	−	0.367517i	−0.0835788	−	0.0474462i
$61$	−1.27699			−0.163502			−0.0817512	−	0.996653i	$-0.526051\pi$
$61$	−1.27699			−0.163502			−0.0817512	+	0.996653i	$0.526051\pi$
$62$		−	9.77838i		−	1.24185i
$63$		−	10.1507i		−	1.27886i
$64$	−1.00000			−0.125000
$65$	13.8563	+	7.86596i	1.71866	+	0.975652i
$66$	0.0965628			0.0118861
$67$			6.04334i			0.738312i	0.929368	+	0.369156i	$0.120353\pi$
$67$			6.04334i			0.738312i	−0.929368	+	0.369156i	$0.879647\pi$
$68$			6.17921i			0.749339i
$69$	2.15060			0.258902
$70$	3.87841	−	6.83201i	0.463559	−	0.816581i
$71$	13.4995			1.60210			0.801050	−	0.598597i	$-0.204275\pi$
$71$	13.4995			1.60210			0.801050	+	0.598597i	$0.204275\pi$
$72$			2.88916i			0.340491i
$73$		−	1.71348i		−	0.200548i	−0.994960	−	0.100274i	$-0.968028\pi$
$73$		−	1.71348i		−	0.200548i	0.994960	−	0.100274i	$-0.0319719\pi$
$74$	−1.00000			−0.116248
$75$	−1.42933	+	0.853215i	−0.165045	+	0.0985208i
$76$	5.83553			0.669381
$77$			1.01903i			0.116129i
$78$			2.37228i			0.268608i
$79$	−8.25422			−0.928672			−0.464336	−	0.885659i	$-0.653707\pi$
$79$	−8.25422			−0.928672			−0.464336	+	0.885659i	$0.653707\pi$
$80$	−1.10390	+	1.94458i	−0.123420	+	0.217411i
$81$	8.01474			0.890526
$82$		−	1.64077i		−	0.181193i
$83$		−	2.41807i		−	0.265418i	−0.991155	−	0.132709i	$-0.957632\pi$
$83$		−	2.41807i		−	0.265418i	0.991155	−	0.132709i	$-0.0423676\pi$
$84$	1.16968			0.127623
$85$	12.0160	+	6.82126i	1.30331	+	0.739869i
$86$	5.34889			0.576785
$87$		−	0.392995i		−	0.0421335i
$88$		−	0.290044i		−	0.0309188i
$89$	10.2797			1.08965			0.544823	−	0.838551i	$-0.316597\pi$
$89$	10.2797			1.08965			0.544823	+	0.838551i	$0.316597\pi$
$90$	5.61821	+	3.18936i	0.592211	+	0.336188i
$91$	−25.0347			−2.62435
$92$		−	6.45973i		−	0.673473i
$93$		−	3.25546i		−	0.337576i
$94$	5.69256			0.587143
$95$	6.44187	−	11.3477i	0.660922	−	1.16425i
$96$	−0.332924			−0.0339790
$97$			15.1272i			1.53594i	0.640489	+	0.767968i	$0.278732\pi$
$97$			15.1272i			1.53594i	−0.640489	+	0.767968i	$0.721268\pi$
$98$			5.34367i			0.539793i
$99$	−0.837984			−0.0842206
$100$	2.56279	+	4.29326i	0.256279	+	0.429326i
$101$	2.63730			0.262421			0.131210	−	0.991355i	$-0.458114\pi$
$101$	2.63730			0.262421			0.131210	+	0.991355i	$0.458114\pi$
$102$			2.05721i			0.203694i
$103$			1.72469i			0.169939i	0.996384	+	0.0849695i	$0.0270793\pi$
$103$			1.72469i			0.169939i	−0.996384	+	0.0849695i	$0.972921\pi$
$104$	7.12558			0.698720
$105$	1.29122	−	2.27454i	0.126010	−	0.221973i
$106$	−9.32034			−0.905271
$107$			10.0279i			0.969438i	0.874670	+	0.484719i	$0.161078\pi$
$107$			10.0279i			0.969438i	−0.874670	+	0.484719i	$0.838922\pi$
$108$			1.96065i			0.188663i
$109$	−4.87361			−0.466807			−0.233403	−	0.972380i	$-0.574986\pi$
$109$	−4.87361			−0.466807			−0.233403	+	0.972380i	$0.574986\pi$
$110$	−0.564014	−	0.320181i	−0.0537767	−	0.0305281i
$111$	−0.332924			−0.0315998
$112$		−	3.51336i		−	0.331981i
$113$			15.9290i			1.49847i	0.662303	+	0.749236i	$0.269579\pi$
$113$			15.9290i			1.49847i	−0.662303	+	0.749236i	$0.730421\pi$
$114$	1.94279			0.181959
$115$	−12.5615	−	7.13092i	−1.17136	−	0.664962i
$116$	−1.18043			−0.109600
$117$		−	20.5869i		−	1.90326i
$118$			5.94279i			0.547078i
$119$	−21.7098			−1.99013
$120$	−0.367517	+	0.647398i	−0.0335496	+	0.0590991i
$121$	−10.9159			−0.992352
$122$			1.27699i			0.115614i
$123$		−	0.546253i		−	0.0492540i
$124$	−9.77838			−0.878124
$125$	11.1777	−	0.244192i	0.999761	−	0.0218412i
$126$	−10.1507			−0.904292
$127$			1.31265i			0.116479i	0.998303	+	0.0582395i	$0.0185487\pi$
$127$			1.31265i			0.116479i	−0.998303	+	0.0582395i	$0.981451\pi$
$128$			1.00000i			0.0883883i
$129$	1.78078			0.156789
$130$	7.86596	−	13.8563i	0.689890	−	1.21527i
$131$	2.41562			0.211054			0.105527	−	0.994416i	$-0.466347\pi$
$131$	2.41562			0.211054			0.105527	+	0.994416i	$0.466347\pi$
$132$		−	0.0965628i		−	0.00840471i
$133$			20.5023i			1.77778i
$134$	6.04334			0.522065
$135$	3.81263	+	2.16437i	0.328139	+	0.186279i
$136$	6.17921			0.529862
$137$			6.87366i			0.587256i	0.955920	+	0.293628i	$0.0948627\pi$
$137$			6.87366i			0.587256i	−0.955920	+	0.293628i	$0.905137\pi$
$138$		−	2.15060i		−	0.183071i
$139$	9.80616			0.831748			0.415874	−	0.909422i	$-0.363476\pi$
$139$	9.80616			0.831748			0.415874	+	0.909422i	$0.363476\pi$
$140$	−6.83201	−	3.87841i	−0.577410	−	0.327786i
$141$	1.89519			0.159604
$142$		−	13.4995i		−	1.13286i
$143$			2.06673i			0.172829i
$144$	2.88916			0.240763
$145$	−1.30308	+	2.29545i	−0.108215	+	0.190626i
$146$	−1.71348			−0.141809
$147$			1.77904i			0.146733i
$148$			1.00000i			0.0821995i
$149$	9.07687			0.743606			0.371803	−	0.928312i	$-0.378740\pi$
$149$	9.07687			0.743606			0.371803	+	0.928312i	$0.378740\pi$
$150$	0.853215	+	1.42933i	0.0696647	+	0.116705i
$151$	20.1964			1.64356			0.821780	−	0.569805i	$-0.192981\pi$
$151$	20.1964			1.64356			0.821780	+	0.569805i	$0.192981\pi$
$152$		−	5.83553i		−	0.473324i
$153$		−	17.8527i		−	1.44331i
$154$	1.01903			0.0821157
$155$	−10.7944	+	19.0148i	−0.867027	+	1.52731i
$156$	2.37228			0.189934
$157$		−	17.2677i		−	1.37811i	−0.724707	−	0.689057i	$-0.758025\pi$
$157$		−	17.2677i		−	1.37811i	0.724707	−	0.689057i	$-0.241975\pi$
$158$			8.25422i			0.656670i
$159$	−3.10297			−0.246081
$160$	1.94458	+	1.10390i	0.153733	+	0.0872713i
$161$	22.6953			1.78864
$162$		−	8.01474i		−	0.629697i
$163$		−	16.6901i		−	1.30727i	−0.756810	−	0.653634i	$-0.773243\pi$
$163$		−	16.6901i		−	1.30727i	0.756810	−	0.653634i	$-0.226757\pi$
$164$	−1.64077			−0.128123
$165$	−0.187774	−	0.106596i	−0.0146182	−	0.00829850i
$166$	−2.41807			−0.187679
$167$			1.47354i			0.114026i	0.998373	+	0.0570130i	$0.0181577\pi$
$167$			1.47354i			0.114026i	−0.998373	+	0.0570130i	$0.981842\pi$
$168$		−	1.16968i		−	0.0902430i
$169$	−37.7738			−2.90568
$170$	6.82126	−	12.0160i	0.523166	−	0.921582i
$171$	−16.8598			−1.28930
$172$		−	5.34889i		−	0.407849i
$173$		−	13.8432i		−	1.05248i	−0.850336	−	0.526240i	$-0.823601\pi$
$173$		−	13.8432i		−	1.05248i	0.850336	−	0.526240i	$-0.176399\pi$
$174$	−0.392995			−0.0297929
$175$	−15.0838	+	9.00399i	−1.14023	+	0.680637i
$176$	−0.290044			−0.0218629
$177$			1.97850i			0.148713i
$178$		−	10.2797i		−	0.770496i
$179$	−21.7817			−1.62804			−0.814020	−	0.580836i	$-0.802726\pi$
$179$	−21.7817			−1.62804			−0.814020	+	0.580836i	$0.802726\pi$
$180$	3.18936	−	5.61821i	0.237721	−	0.418756i
$181$	2.03100			0.150963			0.0754817	−	0.997147i	$-0.475951\pi$
$181$	2.03100			0.150963			0.0754817	+	0.997147i	$0.475951\pi$
$182$			25.0347i			1.85569i
$183$			0.425143i			0.0314275i
$184$	−6.45973			−0.476217
$185$	1.94458	+	1.10390i	0.142968	+	0.0811607i
$186$	−3.25546			−0.238702
$187$			1.79224i			0.131062i
$188$		−	5.69256i		−	0.415173i
$189$	−6.88845			−0.501061
$190$	−11.3477	−	6.44187i	−0.823246	−	0.467343i
$191$	−8.44668			−0.611180			−0.305590	−	0.952163i	$-0.598854\pi$
$191$	−8.44668			−0.611180			−0.305590	+	0.952163i	$0.598854\pi$
$192$			0.332924i			0.0240268i
$193$		−	3.64159i		−	0.262127i	−0.991374	−	0.131064i	$-0.958161\pi$
$193$		−	3.64159i		−	0.262127i	0.991374	−	0.131064i	$-0.0418392\pi$
$194$	15.1272			1.08607
$195$	2.61877	−	4.61309i	0.187534	−	0.330350i
$196$	5.34367			0.381691
$197$			10.1939i			0.726288i	0.931733	+	0.363144i	$0.118297\pi$
$197$			10.1939i			0.726288i	−0.931733	+	0.363144i	$0.881703\pi$
$198$			0.837984i			0.0595530i
$199$	5.25299			0.372375			0.186187	−	0.982514i	$-0.440387\pi$
$199$	5.25299			0.372375			0.186187	+	0.982514i	$0.440387\pi$
$200$	4.29326	−	2.56279i	0.303580	−	0.181216i
$201$	2.01198			0.141914
$202$		−	2.63730i		−	0.185560i
$203$		−	4.14728i		−	0.291082i
$204$	2.05721			0.144033
$205$	−1.81125	+	3.19061i	−0.126504	+	0.222842i
$206$	1.72469			0.120165
$207$			18.6632i			1.29718i
$208$		−	7.12558i		−	0.494070i
$209$	1.69256			0.117077
$210$	−2.27454	−	1.29122i	−0.156958	−	0.0891025i
$211$	−4.81998			−0.331821			−0.165910	−	0.986141i	$-0.553056\pi$
$211$	−4.81998			−0.331821			−0.165910	+	0.986141i	$0.553056\pi$
$212$			9.32034i			0.640123i
$213$		−	4.49433i		−	0.307946i
$214$	10.0279			0.685496
$215$	−10.4013	−	5.90466i	−0.709366	−	0.402695i
$216$	1.96065			0.133405
$217$		−	34.3549i		−	2.33216i
$218$			4.87361i			0.330082i
$219$	−0.570460			−0.0385481
$220$	−0.320181	+	0.564014i	−0.0215866	+	0.0380258i
$221$	−44.0304			−2.96180
$222$			0.332924i			0.0223444i
$223$		−	3.70392i		−	0.248033i	−0.992280	−	0.124017i	$-0.960422\pi$
$223$		−	3.70392i		−	0.248033i	0.992280	−	0.124017i	$-0.0395776\pi$
$224$	−3.51336			−0.234746
$225$	−7.40431	−	12.4039i	−0.493620	−	0.826929i
$226$	15.9290			1.05958
$227$			6.31512i			0.419149i	0.977793	+	0.209575i	$0.0672079\pi$
$227$			6.31512i			0.419149i	−0.977793	+	0.209575i	$0.932792\pi$
$228$		−	1.94279i		−	0.128664i
$229$	20.5548			1.35830			0.679150	−	0.734000i	$-0.262349\pi$
$229$	20.5548			1.35830			0.679150	+	0.734000i	$0.262349\pi$
$230$	−7.13092	+	12.5615i	−0.470199	+	0.828278i
$231$	0.339260			0.0223216
$232$			1.18043i			0.0774992i
$233$		−	21.4393i		−	1.40453i	−0.711914	−	0.702267i	$-0.752171\pi$
$233$		−	21.4393i		−	1.40453i	0.711914	−	0.702267i	$-0.247829\pi$
$234$	−20.5869			−1.34581
$235$	−11.0696	−	6.28405i	−0.722104	−	0.409926i
$236$	5.94279			0.386843
$237$			2.74803i			0.178504i
$238$			21.7098i			1.40723i
$239$	20.7479			1.34207			0.671034	−	0.741426i	$-0.265850\pi$
$239$	20.7479			1.34207			0.671034	+	0.741426i	$0.265850\pi$
$240$	0.647398	+	0.367517i	0.0417894	+	0.0237231i
$241$	10.7731			0.693957			0.346978	−	0.937873i	$-0.387208\pi$
$241$	10.7731			0.693957			0.346978	+	0.937873i	$0.387208\pi$
$242$			10.9159i			0.701699i
$243$		−	8.55024i		−	0.548498i
$244$	1.27699			0.0817512
$245$	5.89891	−	10.3912i	0.376867	−	0.663870i
$246$	−0.546253			−0.0348278
$247$			41.5815i			2.64577i
$248$			9.77838i			0.620927i
$249$	−0.805036			−0.0510171
$250$	−0.244192	−	11.1777i	−0.0154440	−	0.706938i
$251$	−4.46812			−0.282025			−0.141013	−	0.990008i	$-0.545036\pi$
$251$	−4.46812			−0.282025			−0.141013	+	0.990008i	$0.545036\pi$
$252$			10.1507i			0.639431i
$253$		−	1.87361i		−	0.117793i
$254$	1.31265			0.0823631
$255$	2.27096	−	4.00041i	0.142213	−	0.250515i
$256$	1.00000			0.0625000
$257$		−	1.24594i		−	0.0777194i	−0.999245	−	0.0388597i	$-0.987627\pi$
$257$		−	1.24594i		−	0.0777194i	0.999245	−	0.0388597i	$-0.0123725\pi$
$258$		−	1.78078i		−	0.110866i
$259$	−3.51336			−0.218309
$260$	−13.8563	−	7.86596i	−0.859329	−	0.487826i
$261$	3.41046			0.211102
$262$		−	2.41562i		−	0.149237i
$263$		−	16.3230i		−	1.00652i	−0.864135	−	0.503259i	$-0.832134\pi$
$263$		−	16.3230i		−	1.00652i	0.864135	−	0.503259i	$-0.167866\pi$
$264$	−0.0965628			−0.00594303
$265$	18.1241	+	10.2888i	1.11336	+	0.632034i
$266$	20.5023			1.25708
$267$		−	3.42236i		−	0.209445i
$268$		−	6.04334i		−	0.369156i
$269$	18.5763			1.13262			0.566309	−	0.824193i	$-0.308371\pi$
$269$	18.5763			1.13262			0.566309	+	0.824193i	$0.308371\pi$
$270$	2.16437	−	3.81263i	0.131719	−	0.232030i
$271$	16.4181			0.997327			0.498663	−	0.866796i	$-0.333824\pi$
$271$	16.4181			0.997327			0.498663	+	0.866796i	$0.333824\pi$
$272$		−	6.17921i		−	0.374669i
$273$			8.33466i			0.504437i
$274$	6.87366			0.415253
$275$	0.743322	+	1.24524i	0.0448240	+	0.0750906i
$276$	−2.15060			−0.129451
$277$			15.6104i			0.937937i	0.883215	+	0.468968i	$0.155374\pi$
$277$			15.6104i			0.937937i	−0.883215	+	0.468968i	$0.844626\pi$
$278$		−	9.80616i		−	0.588134i
$279$	28.2513			1.69136
$280$	−3.87841	+	6.83201i	−0.231779	+	0.408290i
$281$	−21.8665			−1.30445			−0.652224	−	0.758026i	$-0.726164\pi$
$281$	−21.8665			−1.30445			−0.652224	+	0.758026i	$0.726164\pi$
$282$		−	1.89519i		−	0.112857i
$283$			2.24778i			0.133616i	0.997766	+	0.0668082i	$0.0212816\pi$
$283$			2.24778i			0.133616i	−0.997766	+	0.0668082i	$0.978718\pi$
$284$	−13.4995			−0.801050
$285$	−3.77791	−	2.14466i	−0.223784	−	0.127039i
$286$	2.06673			0.122208
$287$		−	5.76461i		−	0.340274i
$288$		−	2.88916i		−	0.170245i
$289$	−21.1826			−1.24603
$290$	2.29545	+	1.30308i	0.134793	+	0.0765198i
$291$	5.03622			0.295228
$292$			1.71348i			0.100274i
$293$			26.8794i			1.57031i	0.619297	+	0.785157i	$0.287418\pi$
$293$			26.8794i			1.57031i	−0.619297	+	0.785157i	$0.712582\pi$
$294$	1.77904			0.103756
$295$	6.56028	−	11.5562i	0.381954	−	0.672830i
$296$	1.00000			0.0581238
$297$			0.568674i			0.0329978i
$298$		−	9.07687i		−	0.525809i
$299$	46.0293			2.66194
$300$	1.42933	−	0.853215i	0.0825226	−	0.0492604i
$301$	18.7926			1.08318
$302$		−	20.1964i		−	1.16217i
$303$		−	0.878021i		−	0.0504410i
$304$	−5.83553			−0.334691
$305$	1.40968	−	2.48322i	0.0807181	−	0.142189i
$306$	−17.8527			−1.02057
$307$		−	23.9979i		−	1.36963i	−0.728717	−	0.684815i	$-0.759883\pi$
$307$		−	23.9979i		−	1.36963i	0.728717	−	0.684815i	$-0.240117\pi$
$308$		−	1.01903i		−	0.0580645i
$309$	0.574192			0.0326647
$310$	19.0148	+	10.7944i	1.07997	+	0.613081i
$311$	−5.07563			−0.287812			−0.143906	−	0.989591i	$-0.545966\pi$
$311$	−5.07563			−0.287812			−0.143906	+	0.989591i	$0.545966\pi$
$312$		−	2.37228i		−	0.134304i
$313$		−	8.96950i		−	0.506986i	−0.967337	−	0.253493i	$-0.918420\pi$
$313$		−	8.96950i		−	0.506986i	0.967337	−	0.253493i	$-0.0815795\pi$
$314$	−17.2677			−0.974474
$315$	19.7388	+	11.2054i	1.11215	+	0.631350i
$316$	8.25422			0.464336
$317$			22.0181i			1.23666i	0.785918	+	0.618330i	$0.212191\pi$
$317$			22.0181i			1.23666i	−0.785918	+	0.618330i	$0.787809\pi$
$318$			3.10297i			0.174006i
$319$	−0.342377			−0.0191695
$320$	1.10390	−	1.94458i	0.0617102	−	0.108705i
$321$	3.33855			0.186339
$322$		−	22.6953i		−	1.26476i
$323$			36.0589i			2.00637i
$324$	−8.01474			−0.445263
$325$	−30.5920	+	18.2613i	−1.69694	+	1.01296i
$326$	−16.6901			−0.924379
$327$			1.62254i			0.0897268i
$328$			1.64077i			0.0905964i
$329$	20.0000			1.10264
$330$	−0.106596	+	0.187774i	−0.00586793	+	0.0103366i
$331$	−10.7134			−0.588864			−0.294432	−	0.955672i	$-0.595130\pi$
$331$	−10.7134			−0.588864			−0.294432	+	0.955672i	$0.595130\pi$
$332$			2.41807i			0.132709i
$333$		−	2.88916i		−	0.158325i
$334$	1.47354			0.0806286
$335$	−11.7518	−	6.67127i	−0.642067	−	0.364491i
$336$	−1.16968			−0.0638114
$337$		−	1.34097i		−	0.0730471i	−0.999333	−	0.0365235i	$-0.988372\pi$
$337$		−	1.34097i		−	0.0730471i	0.999333	−	0.0365235i	$-0.0116284\pi$
$338$			37.7738i			2.05463i
$339$	5.30315			0.288027
$340$	−12.0160	−	6.82126i	−0.651657	−	0.369935i
$341$	−2.83616			−0.153587
$342$			16.8598i			0.911673i
$343$		−	5.81926i		−	0.314211i
$344$	−5.34889			−0.288393
$345$	−2.37406	+	4.18202i	−0.127815	+	0.225152i
$346$	−13.8432			−0.744216
$347$		−	0.883744i		−	0.0474419i	−0.999719	−	0.0237209i	$-0.992449\pi$
$347$		−	0.883744i		−	0.0474419i	0.999719	−	0.0237209i	$-0.00755131\pi$
$348$			0.392995i			0.0210667i
$349$	9.00521			0.482038			0.241019	−	0.970520i	$-0.422518\pi$
$349$	9.00521			0.482038			0.241019	+	0.970520i	$0.422518\pi$
$350$	9.00399	+	15.0838i	0.481283	+	0.806261i
$351$	−13.9707			−0.745702
$352$			0.290044i			0.0154594i
$353$			6.79030i			0.361411i	0.983537	+	0.180706i	$0.0578381\pi$
$353$			6.79030i			0.361411i	−0.983537	+	0.180706i	$0.942162\pi$
$354$	1.97850			0.105156
$355$	−14.9022	+	26.2509i	−0.790927	+	1.39326i
$356$	−10.2797			−0.544823
$357$			7.22771i			0.382531i
$358$			21.7817i			1.15120i
$359$	10.2263			0.539722			0.269861	−	0.962899i	$-0.413022\pi$
$359$	10.2263			0.539722			0.269861	+	0.962899i	$0.413022\pi$
$360$	−5.61821	−	3.18936i	−0.296106	−	0.168094i
$361$	15.0534			0.792286
$362$		−	2.03100i		−	0.106747i
$363$			3.63416i			0.190744i
$364$	25.0347			1.31217
$365$	3.33200	+	1.89152i	0.174405	+	0.0990067i
$366$	0.425143			0.0222226
$367$		−	17.1583i		−	0.895657i	−0.894119	−	0.447829i	$-0.852198\pi$
$367$		−	17.1583i		−	0.895657i	0.894119	−	0.447829i	$-0.147802\pi$
$368$			6.45973i			0.336737i
$369$	4.74045			0.246778
$370$	1.10390	−	1.94458i	0.0573893	−	0.101094i
$371$	−32.7457			−1.70007
$372$			3.25546i			0.168788i
$373$			17.1601i			0.888515i	0.895899	+	0.444257i	$0.146532\pi$
$373$			17.1601i			0.888515i	−0.895899	+	0.444257i	$0.853468\pi$
$374$	1.79224			0.0926747
$375$	−0.0812974	−	3.72132i	−0.00419818	−	0.192168i
$376$	−5.69256			−0.293571
$377$		−	8.41126i		−	0.433202i
$378$			6.88845i			0.354304i
$379$	27.5435			1.41482			0.707408	−	0.706805i	$-0.249864\pi$
$379$	27.5435			1.41482			0.707408	+	0.706805i	$0.249864\pi$
$380$	−6.44187	+	11.3477i	−0.330461	+	0.582123i
$381$	0.437014			0.0223889
$382$			8.44668i			0.432170i
$383$		−	3.49954i		−	0.178818i	−0.995995	−	0.0894091i	$-0.971502\pi$
$383$		−	3.49954i		−	0.178818i	0.995995	−	0.0894091i	$-0.0284979\pi$
$384$	0.332924			0.0169895
$385$	−1.98158	−	1.12491i	−0.100991	−	0.0573308i
$386$	−3.64159			−0.185352
$387$			15.4538i			0.785561i
$388$		−	15.1272i		−	0.767968i
$389$	13.0015			0.659203			0.329602	−	0.944120i	$-0.393086\pi$
$389$	13.0015			0.659203			0.329602	+	0.944120i	$0.393086\pi$
$390$	−4.61309	−	2.61877i	−0.233593	−	0.132607i
$391$	39.9160			2.01864
$392$		−	5.34367i		−	0.269896i
$393$		−	0.804219i		−	0.0405675i
$394$	10.1939			0.513563
$395$	9.11187	−	16.0510i	0.458468	−	0.807613i
$396$	0.837984			0.0421103
$397$		−	26.6658i		−	1.33832i	−0.743118	−	0.669160i	$-0.766654\pi$
$397$		−	26.6658i		−	1.33832i	0.743118	−	0.669160i	$-0.233346\pi$
$398$		−	5.25299i		−	0.263309i
$399$	6.82572			0.341713
$400$	−2.56279	−	4.29326i	−0.128139	−	0.214663i
$401$	20.3546			1.01646			0.508231	−	0.861221i	$-0.330300\pi$
$401$	20.3546			1.01646			0.508231	+	0.861221i	$0.330300\pi$
$402$		−	2.01198i		−	0.100348i
$403$		−	69.6766i		−	3.47084i
$404$	−2.63730			−0.131210
$405$	−8.84751	+	15.5853i	−0.439636	+	0.774440i
$406$	−4.14728			−0.205826
$407$			0.290044i			0.0143770i
$408$		−	2.05721i		−	0.101847i
$409$	−29.9603			−1.48144			−0.740720	−	0.671814i	$-0.765515\pi$
$409$	−29.9603			−1.48144			−0.740720	+	0.671814i	$0.765515\pi$
$410$	3.19061	+	1.81125i	0.157573	+	0.0894515i
$411$	2.28841			0.112879
$412$		−	1.72469i		−	0.0849695i
$413$			20.8791i			1.02740i
$414$	18.6632			0.917246
$415$	4.70214	+	2.66932i	0.230819	+	0.131032i
$416$	−7.12558			−0.349360
$417$		−	3.26471i		−	0.159874i
$418$		−	1.69256i		−	0.0827859i
$419$	−23.3149			−1.13901			−0.569504	−	0.821988i	$-0.692865\pi$
$419$	−23.3149			−1.13901			−0.569504	+	0.821988i	$0.692865\pi$
$420$	−1.29122	+	2.27454i	−0.0630050	+	0.110986i
$421$	24.0289			1.17110			0.585548	−	0.810638i	$-0.300880\pi$
$421$	24.0289			1.17110			0.585548	+	0.810638i	$0.300880\pi$
$422$			4.81998i			0.234633i
$423$			16.4467i			0.799667i
$424$	9.32034			0.452636
$425$	−26.5290	+	15.8360i	−1.28684	+	0.768158i
$426$	−4.49433			−0.217751
$427$			4.48654i			0.217119i
$428$		−	10.0279i		−	0.484719i
$429$	0.688066			0.0332201
$430$	−5.90466	+	10.4013i	−0.284748	+	0.501597i
$431$	−19.2917			−0.929247			−0.464624	−	0.885508i	$-0.653810\pi$
$431$	−19.2917			−0.929247			−0.464624	+	0.885508i	$0.653810\pi$
$432$		−	1.96065i		−	0.0943316i
$433$			12.5816i			0.604634i	0.953207	+	0.302317i	$0.0977601\pi$
$433$			12.5816i			0.604634i	−0.953207	+	0.302317i	$0.902240\pi$
$434$	−34.3549			−1.64909
$435$	0.764210	+	0.433829i	0.0366411	+	0.0208005i
$436$	4.87361			0.233403
$437$		−	37.6959i		−	1.80324i
$438$			0.570460i			0.0272576i
$439$	−14.0428			−0.670225			−0.335113	−	0.942178i	$-0.608774\pi$
$439$	−14.0428			−0.670225			−0.335113	+	0.942178i	$0.608774\pi$
$440$	0.564014	+	0.320181i	0.0268883	+	0.0152640i
$441$	−15.4387			−0.735178
$442$			44.0304i			2.09431i
$443$			24.5696i			1.16734i	0.811992	+	0.583668i	$0.198383\pi$
$443$			24.5696i			1.16734i	−0.811992	+	0.583668i	$0.801617\pi$
$444$	0.332924			0.0157999
$445$	−11.3478	+	19.9897i	−0.537938	+	0.947603i
$446$	−3.70392			−0.175386
$447$		−	3.02191i		−	0.142932i
$448$			3.51336i			0.165990i
$449$	12.7574			0.602061			0.301030	−	0.953615i	$-0.402669\pi$
$449$	12.7574			0.602061			0.301030	+	0.953615i	$0.402669\pi$
$450$	−12.4039	+	7.40431i	−0.584727	+	0.349042i
$451$	−0.475896			−0.0224091
$452$		−	15.9290i		−	0.749236i
$453$		−	6.72387i		−	0.315915i
$454$	6.31512			0.296383
$455$	27.6359	−	48.6820i	1.29559	−	2.28225i
$456$	−1.94279			−0.0909795
$457$			3.34889i			0.156654i	0.996928	+	0.0783272i	$0.0249579\pi$
$457$			3.34889i			0.156654i	−0.996928	+	0.0783272i	$0.975042\pi$
$458$		−	20.5548i		−	0.960463i
$459$	−12.1152			−0.565491
$460$	12.5615	+	7.13092i	0.585681	+	0.332481i
$461$	−0.859501			−0.0400310			−0.0200155	−	0.999800i	$-0.506372\pi$
$461$	−0.859501			−0.0400310			−0.0200155	+	0.999800i	$0.506372\pi$
$462$		−	0.339260i		−	0.0157838i
$463$		−	13.8711i		−	0.644643i	−0.946630	−	0.322321i	$-0.895537\pi$
$463$		−	13.8711i		−	0.644643i	0.946630	−	0.322321i	$-0.104463\pi$
$464$	1.18043			0.0548002
$465$	6.33051	+	3.59372i	0.293570	+	0.166655i
$466$	−21.4393			−0.993155
$467$			40.9281i			1.89392i	0.321344	+	0.946962i	$0.395865\pi$
$467$			40.9281i			1.89392i	−0.321344	+	0.946962i	$0.604135\pi$
$468$			20.5869i			0.951632i
$469$	21.2324			0.980422
$470$	−6.28405	+	11.0696i	−0.289861	+	0.510605i
$471$	−5.74885			−0.264893
$472$		−	5.94279i		−	0.273539i
$473$		−	1.55141i		−	0.0713341i
$474$	2.74803			0.126221
$475$	14.9552	+	25.0535i	0.686193	+	1.14953i
$476$	21.7098			0.995065
$477$		−	26.9280i		−	1.23295i
$478$		−	20.7479i		−	0.948986i
$479$	−8.58990			−0.392483			−0.196241	−	0.980556i	$-0.562874\pi$
$479$	−8.58990			−0.392483			−0.196241	+	0.980556i	$0.562874\pi$
$480$	0.367517	−	0.647398i	0.0167748	−	0.0295496i
$481$	−7.12558			−0.324898
$482$		−	10.7731i		−	0.490702i
$483$		−	7.55583i		−	0.343802i
$484$	10.9159			0.496176
$485$	−29.4161	−	16.6990i	−1.33572	−	0.758263i
$486$	−8.55024			−0.387847
$487$			25.8389i			1.17087i	0.810718	+	0.585436i	$0.199077\pi$
$487$			25.8389i			1.17087i	−0.810718	+	0.585436i	$0.800923\pi$
$488$		−	1.27699i		−	0.0578068i
$489$	−5.55654			−0.251275
$490$	−10.3912	−	5.89891i	−0.469427	−	0.266486i
$491$	11.4864			0.518376			0.259188	−	0.965827i	$-0.416545\pi$
$491$	11.4864			0.518376			0.259188	+	0.965827i	$0.416545\pi$
$492$			0.546253i			0.0246270i
$493$		−	7.29413i		−	0.328511i
$494$	41.5815			1.87084
$495$	0.925055	−	1.62953i	0.0415781	−	0.0732419i
$496$	9.77838			0.439062
$497$		−	47.4287i		−	2.12747i
$498$			0.805036i			0.0360745i
$499$	9.74599			0.436290			0.218145	−	0.975916i	$-0.429999\pi$
$499$	9.74599			0.436290			0.218145	+	0.975916i	$0.429999\pi$
$500$	−11.1777	+	0.244192i	−0.499881	+	0.0109206i
$501$	0.490578			0.0219174
$502$			4.46812i			0.199422i
$503$		−	17.4803i		−	0.779408i	−0.920940	−	0.389704i	$-0.872577\pi$
$503$		−	17.4803i		−	0.779408i	0.920940	−	0.389704i	$-0.127423\pi$
$504$	10.1507			0.452146
$505$	−2.91133	+	5.12844i	−0.129552	+	0.228212i
$506$	−1.87361			−0.0832920
$507$			12.5758i			0.558512i
$508$		−	1.31265i		−	0.0582395i
$509$	16.3273			0.723695			0.361847	−	0.932237i	$-0.382146\pi$
$509$	16.3273			0.723695			0.361847	+	0.932237i	$0.382146\pi$
$510$	−4.00041	−	2.27096i	−0.177141	−	0.100560i
$511$	−6.02007			−0.266312
$512$		−	1.00000i		−	0.0441942i
$513$			11.4414i			0.505151i
$514$	−1.24594			−0.0549559
$515$	−3.35380	−	1.90390i	−0.147786	−	0.0838957i
$516$	−1.78078			−0.0783943
$517$		−	1.65109i		−	0.0726151i
$518$			3.51336i			0.154368i
$519$	−4.60875			−0.202301
$520$	−7.86596	+	13.8563i	−0.344945	+	0.607637i
$521$	−4.78335			−0.209562			−0.104781	−	0.994495i	$-0.533414\pi$
$521$	−4.78335			−0.209562			−0.104781	+	0.994495i	$0.533414\pi$
$522$		−	3.41046i		−	0.149272i
$523$			24.1224i			1.05480i	0.849618	+	0.527399i	$0.176833\pi$
$523$			24.1224i			1.05480i	−0.849618	+	0.527399i	$0.823167\pi$
$524$	−2.41562			−0.105527
$525$	2.99765	+	5.02176i	0.130828	+	0.219167i
$526$	−16.3230			−0.711716
$527$		−	60.4226i		−	2.63205i
$528$			0.0965628i			0.00420236i
$529$	−18.7281			−0.814264
$530$	10.2888	−	18.1241i	0.446915	−	0.787263i
$531$	−17.1697			−0.745101
$532$		−	20.5023i		−	0.888888i
$533$		−	11.6914i		−	0.506412i
$534$	−3.42236			−0.148100
$535$	−19.5001	−	11.0699i	−0.843064	−	0.478593i
$536$	−6.04334			−0.261033
$537$			7.25166i			0.312932i
$538$		−	18.5763i		−	0.800881i
$539$	1.54990			0.0667590
$540$	−3.81263	−	2.16437i	−0.164070	−	0.0931395i
$541$	4.11745			0.177023			0.0885115	−	0.996075i	$-0.471789\pi$
$541$	4.11745			0.177023			0.0885115	+	0.996075i	$0.471789\pi$
$542$		−	16.4181i		−	0.705217i
$543$		−	0.676171i		−	0.0290173i
$544$	−6.17921			−0.264931
$545$	5.38000	−	9.47712i	0.230454	−	0.405955i
$546$	8.33466			0.356691
$547$			9.22742i			0.394536i	0.980350	+	0.197268i	$0.0632069\pi$
$547$			9.22742i			0.394536i	−0.980350	+	0.197268i	$0.936793\pi$
$548$		−	6.87366i		−	0.293628i
$549$	−3.68944			−0.157462
$550$	1.24524	−	0.743322i	0.0530971	−	0.0316953i
$551$	−6.88845			−0.293458
$552$			2.15060i			0.0915357i
$553$			29.0000i			1.23321i
$554$	15.6104			0.663222
$555$	0.367517	−	0.647398i	0.0156002	−	0.0274805i
$556$	−9.80616			−0.415874
$557$		−	2.25125i		−	0.0953885i	−0.998862	−	0.0476943i	$-0.984813\pi$
$557$		−	2.25125i		−	0.0953885i	0.998862	−	0.0476943i	$-0.0151873\pi$
$558$		−	28.2513i		−	1.19597i
$559$	38.1139			1.61205
$560$	6.83201	+	3.87841i	0.288705	+	0.163893i
$561$	0.596681			0.0251919
$562$			21.8665i			0.922384i
$563$			5.79316i			0.244153i	0.992521	+	0.122076i	$0.0389553\pi$
$563$			5.79316i			0.244153i	−0.992521	+	0.122076i	$0.961045\pi$
$564$	−1.89519			−0.0798020
$565$	−30.9752	−	17.5841i	−1.30314	−	0.739768i
$566$	2.24778			0.0944811
$567$		−	28.1586i		−	1.18255i
$568$			13.4995i			0.566428i
$569$	34.4807			1.44551			0.722753	−	0.691106i	$-0.242876\pi$
$569$	34.4807			1.44551			0.722753	+	0.691106i	$0.242876\pi$
$570$	−2.14466	+	3.77791i	−0.0898298	+	0.158239i
$571$	−19.2152			−0.804133			−0.402066	−	0.915611i	$-0.631708\pi$
$571$	−19.2152			−0.804133			−0.402066	+	0.915611i	$0.631708\pi$
$572$		−	2.06673i		−	0.0864144i
$573$			2.81211i			0.117477i
$574$	−5.76461			−0.240610
$575$	27.7333	−	16.5549i	1.15656	−	0.690387i
$576$	−2.88916			−0.120382
$577$		−	6.33354i		−	0.263669i	−0.991272	−	0.131834i	$-0.957913\pi$
$577$		−	6.33354i		−	0.263669i	0.991272	−	0.131834i	$-0.0420867\pi$
$578$			21.1826i			0.881079i
$579$	−1.21237			−0.0503845
$580$	1.30308	−	2.29545i	0.0541077	−	0.0953132i
$581$	−8.49555			−0.352455
$582$		−	5.03622i		−	0.208758i
$583$			2.70331i			0.111960i
$584$	1.71348			0.0709044
$585$	40.0330	+	22.7260i	1.65516	+	0.939605i
$586$	26.8794			1.11038
$587$			21.9099i			0.904320i	0.891937	+	0.452160i	$0.149346\pi$
$587$			21.9099i			0.904320i	−0.891937	+	0.452160i	$0.850654\pi$
$588$		−	1.77904i		−	0.0733664i
$589$	−57.0620			−2.35120
$590$	−11.5562	−	6.56028i	−0.475763	−	0.270082i
$591$	3.39381			0.139603
$592$		−	1.00000i		−	0.0410997i
$593$		−	9.40482i		−	0.386210i	−0.981178	−	0.193105i	$-0.938144\pi$
$593$		−	9.40482i		−	0.386210i	0.981178	−	0.193105i	$-0.0618557\pi$
$594$	0.568674			0.0233330
$595$	23.9655	−	42.2164i	0.982490	−	1.73070i
$596$	−9.07687			−0.371803
$597$		−	1.74885i		−	0.0715756i
$598$		−	46.0293i		−	1.88228i
$599$	−16.4095			−0.670474			−0.335237	−	0.942134i	$-0.608816\pi$
$599$	−16.4095			−0.670474			−0.335237	+	0.942134i	$0.608816\pi$
$600$	−0.853215	−	1.42933i	−0.0348323	−	0.0583523i
$601$	−7.01392			−0.286104			−0.143052	−	0.989715i	$-0.545692\pi$
$601$	−7.01392			−0.286104			−0.143052	+	0.989715i	$0.545692\pi$
$602$		−	18.7926i		−	0.765927i
$603$			17.4602i			0.711034i
$604$	−20.1964			−0.821780
$605$	12.0501	−	21.2268i	0.489906	−	0.862992i
$606$	−0.878021			−0.0356672
$607$		−	16.5621i		−	0.672234i	−0.941820	−	0.336117i	$-0.890886\pi$
$607$		−	16.5621i		−	0.672234i	0.941820	−	0.336117i	$-0.109114\pi$
$608$			5.83553i			0.236662i
$609$	−1.38073			−0.0559500
$610$	−2.48322	−	1.40968i	−0.100543	−	0.0570763i
$611$	40.5628			1.64099
$612$			17.8527i			0.721653i
$613$			23.9370i			0.966804i	0.875398	+	0.483402i	$0.160599\pi$
$613$			23.9370i			0.966804i	−0.875398	+	0.483402i	$0.839401\pi$
$614$	−23.9979			−0.968475
$615$	1.06223	+	0.603011i	0.0428334	+	0.0243158i
$616$	−1.01903			−0.0410578
$617$			13.9489i			0.561563i	0.959772	+	0.280781i	$0.0905936\pi$
$617$			13.9489i			0.561563i	−0.959772	+	0.280781i	$0.909406\pi$
$618$		−	0.574192i		−	0.0230974i
$619$	−21.6942			−0.871964			−0.435982	−	0.899955i	$-0.643599\pi$
$619$	−21.6942			−0.871964			−0.435982	+	0.899955i	$0.643599\pi$
$620$	10.7944	−	19.0148i	0.433513	−	0.763654i
$621$	12.6652			0.508238
$622$			5.07563i			0.203514i
$623$		−	36.1163i		−	1.44697i
$624$	−2.37228			−0.0949671
$625$	−11.8642	+	22.0055i	−0.474570	+	0.880218i
$626$	−8.96950			−0.358493
$627$		−	0.563495i		−	0.0225038i
$628$			17.2677i			0.689057i
$629$	−6.17921			−0.246381
$630$	11.2054	−	19.7388i	0.446432	−	0.786411i
$631$	−32.4902			−1.29342			−0.646708	−	0.762738i	$-0.723855\pi$
$631$	−32.4902			−1.29342			−0.646708	+	0.762738i	$0.723855\pi$
$632$		−	8.25422i		−	0.328335i
$633$			1.60469i			0.0637806i
$634$	22.0181			0.874451
$635$	−2.55256	−	1.44904i	−0.101295	−	0.0575035i
$636$	3.10297			0.123041
$637$			38.0768i			1.50866i
$638$			0.342377i			0.0135549i
$639$	39.0024			1.54291
$640$	−1.94458	−	1.10390i	−0.0768663	−	0.0436357i
$641$	−28.1621			−1.11234			−0.556168	−	0.831070i	$-0.687729\pi$
$641$	−28.1621			−1.11234			−0.556168	+	0.831070i	$0.687729\pi$
$642$		−	3.33855i		−	0.131762i
$643$			8.32452i			0.328287i	0.986436	+	0.164144i	$0.0524860\pi$
$643$			8.32452i			0.328287i	−0.986436	+	0.164144i	$0.947514\pi$
$644$	−22.6953			−0.894321
$645$	−1.96581	+	3.46286i	−0.0774036	+	0.136350i
$646$	36.0589			1.41872
$647$		−	1.75827i		−	0.0691249i	−0.999403	−	0.0345624i	$-0.988996\pi$
$647$		−	1.75827i		−	0.0691249i	0.999403	−	0.0345624i	$-0.0110038\pi$
$648$			8.01474i			0.314849i
$649$	1.72367			0.0676600
$650$	18.2613	+	30.5920i	0.716269	+	1.19992i
$651$	−11.4376			−0.448275
$652$			16.6901i			0.653634i
$653$			24.7416i			0.968213i	0.875009	+	0.484106i	$0.160855\pi$
$653$			24.7416i			0.968213i	−0.875009	+	0.484106i	$0.839145\pi$
$654$	1.62254			0.0634464
$655$	−2.66661	+	4.69737i	−0.104193	+	0.183541i
$656$	1.64077			0.0640613
$657$		−	4.95053i		−	0.193138i
$658$		−	20.0000i		−	0.779681i
$659$	−18.2640			−0.711466			−0.355733	−	0.934588i	$-0.615769\pi$
$659$	−18.2640			−0.711466			−0.355733	+	0.934588i	$0.615769\pi$
$660$	0.187774	+	0.106596i	0.00730910	+	0.00414925i
$661$	2.61857			0.101851			0.0509253	−	0.998702i	$-0.483783\pi$
$661$	2.61857			0.101851			0.0509253	+	0.998702i	$0.483783\pi$
$662$			10.7134i			0.416390i
$663$			14.6588i			0.569300i
$664$	2.41807			0.0938394
$665$	−39.8684	−	22.6326i	−1.54603	−	0.877654i
$666$	−2.88916			−0.111953
$667$			7.62527i			0.295252i
$668$		−	1.47354i		−	0.0570130i
$669$	−1.23313			−0.0476754
$670$	−6.67127	+	11.7518i	−0.257734	+	0.454010i
$671$	0.370385			0.0142986
$672$			1.16968i			0.0451215i
$673$		−	48.4181i		−	1.86638i	−0.359384	−	0.933190i	$-0.617013\pi$
$673$		−	48.4181i		−	1.86638i	0.359384	−	0.933190i	$-0.382987\pi$
$674$	−1.34097			−0.0516521
$675$	−8.41757	+	5.02472i	−0.323992	+	0.193402i
$676$	37.7738			1.45284
$677$			7.49862i			0.288195i	0.989563	+	0.144098i	$0.0460280\pi$
$677$			7.49862i			0.288195i	−0.989563	+	0.144098i	$0.953972\pi$
$678$		−	5.30315i		−	0.203666i
$679$	53.1473			2.03961
$680$	−6.82126	+	12.0160i	−0.261583	+	0.460791i
$681$	2.10246			0.0805664
$682$			2.83616i			0.108602i
$683$		−	33.2987i		−	1.27414i	−0.770806	−	0.637070i	$-0.780146\pi$
$683$		−	33.2987i		−	1.27414i	0.770806	−	0.637070i	$-0.219854\pi$
$684$	16.8598			0.644650
$685$	−13.3664	−	7.58787i	−0.510703	−	0.289917i
$686$	−5.81926			−0.222181
$687$		−	6.84320i		−	0.261084i
$688$			5.34889i			0.203924i
$689$	−66.4128			−2.53012
$690$	4.18202	+	2.37406i	0.159207	+	0.0903789i
$691$	38.3695			1.45964			0.729822	−	0.683638i	$-0.239603\pi$
$691$	38.3695			1.45964			0.729822	+	0.683638i	$0.239603\pi$
$692$			13.8432i			0.526240i
$693$			2.94414i			0.111839i
$694$	−0.883744			−0.0335465
$695$	−10.8251	+	19.0689i	−0.410618	+	0.723324i
$696$	0.392995			0.0148964
$697$		−	10.1387i		−	0.384029i
$698$		−	9.00521i		−	0.340852i
$699$	−7.13766			−0.269971
$700$	15.0838	−	9.00399i	0.570113	−	0.340319i
$701$	−40.6339			−1.53472			−0.767360	−	0.641217i	$-0.778430\pi$
$701$	−40.6339			−1.53472			−0.767360	+	0.641217i	$0.778430\pi$
$702$			13.9707i			0.527291i
$703$			5.83553i			0.220091i
$704$	0.290044			0.0109315
$705$	−2.09211	+	3.68536i	−0.0787935	+	0.138799i
$706$	6.79030			0.255556
$707$		−	9.26577i		−	0.348475i
$708$		−	1.97850i		−	0.0743566i
$709$	−11.1957			−0.420464			−0.210232	−	0.977651i	$-0.567422\pi$
$709$	−11.1957			−0.420464			−0.210232	+	0.977651i	$0.567422\pi$
$710$	26.2509	+	14.9022i	0.985180	+	0.559270i
$711$	−23.8478			−0.894361
$712$			10.2797i			0.385248i
$713$			63.1656i			2.36557i
$714$	7.22771			0.270490
$715$	−4.01893	−	2.28148i	−0.150299	−	0.0853223i
$716$	21.7817			0.814020
$717$		−	6.90748i		−	0.257964i
$718$		−	10.2263i		−	0.381641i
$719$	−30.2226			−1.12711			−0.563556	−	0.826078i	$-0.690567\pi$
$719$	−30.2226			−1.12711			−0.563556	+	0.826078i	$0.690567\pi$
$720$	−3.18936	+	5.61821i	−0.118860	+	0.209378i
$721$	6.05946			0.225666
$722$		−	15.0534i		−	0.560231i
$723$		−	3.58663i		−	0.133388i
$724$	−2.03100			−0.0754817
$725$	−3.02520	−	5.06791i	−0.112353	−	0.188217i
$726$	3.63416			0.134876
$727$			19.1911i			0.711758i	0.934532	+	0.355879i	$0.115818\pi$
$727$			19.1911i			0.711758i	−0.934532	+	0.355879i	$0.884182\pi$
$728$		−	25.0347i		−	0.927847i
$729$	21.1976			0.785097
$730$	1.89152	−	3.33200i	0.0700083	−	0.123323i
$731$	33.0519			1.22247
$732$		−	0.425143i		−	0.0157137i
$733$			5.39567i			0.199294i	0.995023	+	0.0996468i	$0.0317713\pi$
$733$			5.39567i			0.199294i	−0.995023	+	0.0996468i	$0.968229\pi$
$734$	−17.1583			−0.633325
$735$	−3.45949	−	1.96389i	−0.127605	−	0.0724392i
$736$	6.45973			0.238109
$737$		−	1.75284i		−	0.0645665i
$738$		−	4.74045i		−	0.174498i
$739$	−24.7127			−0.909072			−0.454536	−	0.890728i	$-0.650195\pi$
$739$	−24.7127			−0.909072			−0.454536	+	0.890728i	$0.650195\pi$
$740$	−1.94458	−	1.10390i	−0.0714842	−	0.0405804i
$741$	13.8435			0.508554
$742$			32.7457i			1.20213i
$743$			45.4537i			1.66753i	0.552116	+	0.833767i	$0.313820\pi$
$743$			45.4537i			1.66753i	−0.552116	+	0.833767i	$0.686180\pi$
$744$	3.25546			0.119351
$745$	−10.0200	+	17.6507i	−0.367104	+	0.646672i
$746$	17.1601			0.628275
$747$		−	6.98620i		−	0.255612i
$748$		−	1.79224i		−	0.0655309i
$749$	35.2317			1.28734
$750$	−3.72132	+	0.0812974i	−0.135883	+	0.00296856i
$751$	49.6360			1.81124			0.905621	−	0.424088i	$-0.139405\pi$
$751$	49.6360			1.81124			0.905621	+	0.424088i	$0.139405\pi$
$752$			5.69256i			0.207586i
$753$			1.48755i			0.0542093i
$754$	−8.41126			−0.306320
$755$	−22.2949	+	39.2735i	−0.811395	+	1.42931i
$756$	6.88845			0.250530
$757$			27.9481i			1.01579i	0.861419	+	0.507896i	$0.169576\pi$
$757$			27.9481i			1.01579i	−0.861419	+	0.507896i	$0.830424\pi$
$758$		−	27.5435i		−	1.00043i
$759$	−0.623769			−0.0226414
$760$	11.3477	+	6.44187i	0.411623	+	0.233671i
$761$	−53.4744			−1.93844			−0.969222	−	0.246188i	$-0.920822\pi$
$761$	−53.4744			−1.93844			−0.969222	+	0.246188i	$0.920822\pi$
$762$		−	0.437014i		−	0.0158313i
$763$			17.1227i			0.619884i
$764$	8.44668			0.305590
$765$	34.7161	+	19.7077i	1.25516	+	0.712534i
$766$	−3.49954			−0.126444
$767$			42.3458i			1.52902i
$768$		−	0.332924i		−	0.0120134i
$769$	8.46659			0.305313			0.152657	−	0.988279i	$-0.451217\pi$
$769$	8.46659			0.305313			0.152657	+	0.988279i	$0.451217\pi$
$770$	−1.12491	+	1.98158i	−0.0405390	+	0.0714113i
$771$	−0.414803			−0.0149388
$772$			3.64159i			0.131064i
$773$		−	0.530866i		−	0.0190939i	−0.999954	−	0.00954697i	$-0.996961\pi$
$773$		−	0.530866i		−	0.0190939i	0.999954	−	0.00954697i	$-0.00303894\pi$
$774$	15.4538			0.555475
$775$	−25.0599	−	41.9811i	−0.900178	−	1.50801i
$776$	−15.1272			−0.543035
$777$			1.16968i			0.0419621i
$778$		−	13.0015i		−	0.466127i
$779$	−9.57477			−0.343052
$780$	−2.61877	+	4.61309i	−0.0937670	+	0.165175i
$781$	−3.91546			−0.140106
$782$		−	39.9160i		−	1.42739i
$783$		−	2.31441i		−	0.0827102i
$784$	−5.34367			−0.190846
$785$	33.5785	+	19.0619i	1.19847	+	0.680349i
$786$	−0.804219			−0.0286855
$787$			2.16917i			0.0773227i	0.999252	+	0.0386613i	$0.0123094\pi$
$787$			2.16917i			0.0773227i	−0.999252	+	0.0386613i	$0.987691\pi$
$788$		−	10.1939i		−	0.363144i
$789$	−5.43432			−0.193467
$790$	−16.0510	−	9.11187i	−0.571069	−	0.324186i
$791$	55.9642			1.98986
$792$		−	0.837984i		−	0.0297765i
$793$			9.09932i			0.323126i
$794$	−26.6658			−0.946336
$795$	3.42538	−	6.03397i	0.121486	−	0.214003i
$796$	−5.25299			−0.186187
$797$		−	26.2510i		−	0.929857i	−0.885348	−	0.464928i	$-0.846080\pi$
$797$		−	26.2510i		−	0.929857i	0.885348	−	0.464928i	$-0.153920\pi$
$798$		−	6.82572i		−	0.241628i
$799$	35.1755			1.24442
$800$	−4.29326	+	2.56279i	−0.151790	+	0.0906082i
$801$	29.6997			1.04939
$802$		−	20.3546i		−	0.718747i
$803$			0.496986i			0.0175382i
$804$	−2.01198			−0.0709569
$805$	−25.0535	+	44.1329i	−0.883019	+	1.55548i
$806$	−69.6766			−2.45425
$807$		−	6.18451i		−	0.217705i
$808$			2.63730i			0.0927798i
$809$	−6.67443			−0.234661			−0.117330	−	0.993093i	$-0.537434\pi$
$809$	−6.67443			−0.234661			−0.117330	+	0.993093i	$0.537434\pi$
$810$	15.5853	+	8.84751i	0.547612	+	0.310870i
$811$	−8.24768			−0.289615			−0.144808	−	0.989460i	$-0.546256\pi$
$811$	−8.24768			−0.289615			−0.144808	+	0.989460i	$0.546256\pi$
$812$			4.14728i			0.145541i
$813$		−	5.46598i		−	0.191700i
$814$	0.290044			0.0101660
$815$	32.4552	+	18.4243i	1.13686	+	0.645374i
$816$	−2.05721			−0.0720167
$817$		−	31.2136i		−	1.09203i
$818$			29.9603i			1.04754i
$819$	−72.3292			−2.52739
$820$	1.81125	−	3.19061i	0.0632518	−	0.111421i
$821$	−9.61631			−0.335611			−0.167806	−	0.985820i	$-0.553668\pi$
$821$	−9.61631			−0.335611			−0.167806	+	0.985820i	$0.553668\pi$
$822$		−	2.28841i		−	0.0798174i
$823$			32.7309i			1.14093i	0.821322	+	0.570464i	$0.193237\pi$
$823$			32.7309i			1.14093i	−0.821322	+	0.570464i	$0.806763\pi$
$824$	−1.72469			−0.0600825
$825$	0.414570	−	0.247470i	0.0144335	−	0.00861580i
$826$	20.8791			0.726478
$827$			39.9956i			1.39078i	0.718631	+	0.695391i	$0.244769\pi$
$827$			39.9956i			1.39078i	−0.718631	+	0.695391i	$0.755231\pi$
$828$		−	18.6632i		−	0.648591i
$829$	−36.8620			−1.28027			−0.640134	−	0.768263i	$-0.721121\pi$
$829$	−36.8620			−1.28027			−0.640134	+	0.768263i	$0.721121\pi$
$830$	2.66932	−	4.70214i	0.0926535	−	0.163214i
$831$	5.19708			0.180285
$832$			7.12558i			0.247035i
$833$			33.0197i			1.14406i
$834$	−3.26471			−0.113048
$835$	−2.86542	−	1.62665i	−0.0991620	−	0.0562925i
$836$	−1.69256			−0.0585385
$837$		−	19.1719i		−	0.662679i
$838$			23.3149i			0.805400i
$839$	−36.7629			−1.26919			−0.634597	−	0.772843i	$-0.718834\pi$
$839$	−36.7629			−1.26919			−0.634597	+	0.772843i	$0.718834\pi$
$840$	2.27454	+	1.29122i	0.0784791	+	0.0445513i
$841$	−27.6066			−0.951951
$842$		−	24.0289i		−	0.828089i
$843$			7.27991i			0.250733i
$844$	4.81998			0.165910
$845$	41.6987	−	73.4543i	1.43448	−	2.52690i
$846$	16.4467			0.565450
$847$			38.3514i			1.31777i
$848$		−	9.32034i		−	0.320062i
$849$	0.748340			0.0256830
$850$	15.8360	+	26.5290i	0.543170	+	0.909936i
$851$	6.45973			0.221437
$852$			4.49433i			0.153973i
$853$			15.9547i			0.546278i	0.961975	+	0.273139i	$0.0880619\pi$
$853$			15.9547i			0.546278i	−0.961975	+	0.273139i	$0.911938\pi$
$854$	4.48654			0.153526
$855$	18.6116	−	32.7852i	0.636504	−	1.12123i
$856$	−10.0279			−0.342748
$857$			10.2157i			0.348963i	0.984660	+	0.174481i	$0.0558249\pi$
$857$			10.2157i			0.348963i	−0.984660	+	0.174481i	$0.944175\pi$
$858$		−	0.688066i		−	0.0234902i
$859$	−7.41899			−0.253133			−0.126566	−	0.991958i	$-0.540396\pi$
$859$	−7.41899			−0.253133			−0.126566	+	0.991958i	$0.540396\pi$
$860$	10.4013	+	5.90466i	0.354683	+	0.201347i
$861$	−1.91918			−0.0654055
$862$			19.2917i			0.657077i
$863$			9.35839i			0.318563i	0.987233	+	0.159282i	$0.0509178\pi$
$863$			9.35839i			0.318563i	−0.987233	+	0.159282i	$0.949082\pi$
$864$	−1.96065			−0.0667025
$865$	26.9192	+	15.2816i	0.915282	+	0.519590i
$866$	12.5816			0.427541
$867$			7.05220i			0.239505i
$868$			34.3549i			1.16608i
$869$	2.39409			0.0812139
$870$	0.433829	−	0.764210i	0.0147082	−	0.0259091i
$871$	43.0623			1.45911
$872$		−	4.87361i		−	0.165041i
$873$			43.7050i			1.47919i
$874$	−37.6959			−1.27508
$875$	−0.857933	−	39.2711i	−0.0290034	−	1.32761i
$876$	0.570460			0.0192741
$877$			13.1486i			0.443997i	0.975047	+	0.221998i	$0.0712580\pi$
$877$			13.1486i			0.443997i	−0.975047	+	0.221998i	$0.928742\pi$
$878$			14.0428i			0.473921i
$879$	8.94882			0.301836
$880$	0.320181	−	0.564014i	0.0107933	−	0.0190129i
$881$	26.7781			0.902178			0.451089	−	0.892479i	$-0.351036\pi$
$881$	26.7781			0.902178			0.451089	+	0.892479i	$0.351036\pi$
$882$			15.4387i			0.519849i
$883$		−	16.7245i		−	0.562824i	−0.959587	−	0.281412i	$-0.909197\pi$
$883$		−	16.7245i		−	0.562824i	0.959587	−	0.281412i	$-0.0908028\pi$
$884$	44.0304			1.48090
$885$	−3.84735	−	2.18408i	−0.129327	−	0.0734169i
$886$	24.5696			0.825432
$887$		−	18.1469i		−	0.609312i	−0.952462	−	0.304656i	$-0.901458\pi$
$887$		−	18.1469i		−	0.609312i	0.952462	−	0.304656i	$-0.0985415\pi$
$888$		−	0.332924i		−	0.0111722i
$889$	4.61181			0.154675
$890$	19.9897	+	11.3478i	0.670057	+	0.380380i
$891$	−2.32463			−0.0778780
$892$			3.70392i			0.124017i
$893$		−	33.2191i		−	1.11164i
$894$	−3.02191			−0.101068
$895$	24.0449	−	42.3563i	0.803733	−	1.41581i
$896$	3.51336			0.117373
$897$		−	15.3243i		−	0.511663i
$898$		−	12.7574i		−	0.425721i
$899$	11.5427			0.384971
$900$	7.40431	+	12.4039i	0.246810	+	0.413464i
$901$	−57.5923			−1.91868
$902$			0.475896i			0.0158456i
$903$		−	6.25650i		−	0.208203i
$904$	−15.9290			−0.529790
$905$	−2.24204	+	3.94945i	−0.0745278	+	0.131284i
$906$	−6.72387			−0.223386
$907$		−	50.1481i		−	1.66514i	−0.553920	−	0.832570i	$-0.686869\pi$
$907$		−	50.1481i		−	1.66514i	0.553920	−	0.832570i	$-0.313131\pi$
$908$		−	6.31512i		−	0.209575i
$909$	7.61958			0.252725
$910$	−48.6820	−	27.6359i	−1.61379	−	0.916122i
$911$	2.64691			0.0876960			0.0438480	−	0.999038i	$-0.486038\pi$
$911$	2.64691			0.0876960			0.0438480	+	0.999038i	$0.486038\pi$
$912$			1.94279i			0.0643322i
$913$			0.701348i			0.0232112i
$914$	3.34889			0.110771
$915$	−0.826725	−	0.469317i	−0.0273307	−	0.0155152i
$916$	−20.5548			−0.679150
$917$		−	8.48693i		−	0.280263i
$918$			12.1152i			0.399862i
$919$	39.5369			1.30420			0.652101	−	0.758132i	$-0.273888\pi$
$919$	39.5369			1.30420			0.652101	+	0.758132i	$0.273888\pi$
$920$	7.13092	−	12.5615i	0.235100	−	0.414139i
$921$	−7.98947			−0.263262
$922$			0.859501i			0.0283062i
$923$		−	96.1920i		−	3.16620i
$924$	−0.339260			−0.0111608
$925$	−4.29326	+	2.56279i	−0.141162	+	0.0842639i
$926$	−13.8711			−0.455831
$927$			4.98292i			0.163660i
$928$		−	1.18043i		−	0.0387496i
$929$	39.2999			1.28939			0.644693	−	0.764441i	$-0.276985\pi$
$929$	39.2999			1.28939			0.644693	+	0.764441i	$0.276985\pi$
$930$	3.59372	−	6.33051i	0.117843	−	0.207585i
$931$	31.1832			1.02199
$932$			21.4393i			0.702267i
$933$			1.68980i			0.0553216i
$934$	40.9281			1.33921
$935$	−3.48516	−	1.97847i	−0.113977	−	0.0647027i
$936$	20.5869			0.672905
$937$			27.7584i			0.906826i	0.891301	+	0.453413i	$0.149794\pi$
$937$			27.7584i			0.906826i	−0.891301	+	0.453413i	$0.850206\pi$
$938$		−	21.2324i		−	0.693263i
$939$	−2.98617			−0.0974499
$940$	11.0696	+	6.28405i	0.361052	+	0.204963i
$941$	48.2212			1.57197			0.785983	−	0.618249i	$-0.212158\pi$
$941$	48.2212			1.57197			0.785983	+	0.618249i	$0.212158\pi$
$942$			5.74885i			0.187308i
$943$			10.5989i			0.345149i
$944$	−5.94279			−0.193421
$945$	7.60419	−	13.3951i	0.247364	−	0.435744i
$946$	−1.55141			−0.0504408
$947$			26.5111i			0.861495i	0.902472	+	0.430748i	$0.141750\pi$
$947$			26.5111i			0.861495i	−0.902472	+	0.430748i	$0.858250\pi$
$948$		−	2.74803i		−	0.0892519i
$949$	−12.2095			−0.396339
$950$	25.0535	−	14.9552i	0.812842	−	0.485212i
$951$	7.33037			0.237703
$952$		−	21.7098i		−	0.703617i
$953$		−	31.8487i		−	1.03168i	−0.856685	−	0.515840i	$-0.827480\pi$
$953$		−	31.8487i		−	1.03168i	0.856685	−	0.515840i	$-0.172520\pi$
$954$	−26.9280			−0.871825
$955$	9.32433	−	16.4252i	0.301728	−	0.531508i
$956$	−20.7479			−0.671034
$957$			0.113986i			0.00368464i
$958$			8.58990i			0.277527i
$959$	24.1496			0.779832
$960$	−0.647398	−	0.367517i	−0.0208947	−	0.0118616i
$961$	64.6166			2.08441
$962$			7.12558i			0.229738i
$963$			28.9723i			0.933620i
$964$	−10.7731			−0.346978
$965$	7.08136	+	4.01997i	0.227957	+	0.129407i
$966$	−7.55583			−0.243105
$967$		−	19.4699i		−	0.626109i	−0.949735	−	0.313054i	$-0.898648\pi$
$967$		−	19.4699i		−	0.626109i	0.949735	−	0.313054i	$-0.101352\pi$
$968$		−	10.9159i		−	0.350849i
$969$	12.0049			0.385653
$970$	−16.6990	+	29.4161i	−0.536173	+	0.944493i
$971$	−21.8178			−0.700168			−0.350084	−	0.936718i	$-0.613847\pi$
$971$	−21.8178			−0.700168			−0.350084	+	0.936718i	$0.613847\pi$
$972$			8.55024i			0.274249i
$973$		−	34.4525i		−	1.10450i
$974$	25.8389			0.827932
$975$	6.07965	+	10.1848i	0.194705	+	0.326175i
$976$	−1.27699			−0.0408756
$977$			41.8705i			1.33956i	0.742561	+	0.669779i	$0.233611\pi$
$977$			41.8705i			1.33956i	−0.742561	+	0.669779i	$0.766389\pi$
$978$			5.55654i			0.177679i
$979$	−2.98157			−0.0952913
$980$	−5.89891	+	10.3912i	−0.188434	+	0.331935i
$981$	−14.0806			−0.449560
$982$		−	11.4864i		−	0.366547i
$983$		−	37.0175i		−	1.18067i	−0.807157	−	0.590337i	$-0.798995\pi$
$983$		−	37.0175i		−	1.18067i	0.807157	−	0.590337i	$-0.201005\pi$
$984$	0.546253			0.0174139
$985$	−19.8229	−	11.2531i	−0.631611	−	0.358555i
$986$	−7.29413			−0.232292
$987$		−	6.65849i		−	0.211942i
$988$		−	41.5815i		−	1.32288i
$989$	−34.5524			−1.09870
$990$	−1.62953	−	0.925055i	−0.0517898	−	0.0294002i
$991$	−28.4749			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$991$	−28.4749			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$992$		−	9.77838i		−	0.310464i
$993$			3.56677i			0.113188i
$994$	−47.4287			−1.50435
$995$	−5.79880	+	10.2149i	−0.183834	+	0.323833i
$996$	0.805036			0.0255085
$997$			14.2442i			0.451118i	0.974229	+	0.225559i	$0.0724209\pi$
$997$			14.2442i			0.451118i	−0.974229	+	0.225559i	$0.927579\pi$
$998$		−	9.74599i		−	0.308504i
$999$	−1.96065			−0.0620321

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.b.d.149.3	✓	10
3.2	odd	2		3330.2.d.p.1999.9		10
5.2	odd	4		1850.2.a.be.1.3		5
5.3	odd	4		1850.2.a.bd.1.3		5
5.4	even	2	inner	370.2.b.d.149.8	yes	10
15.14	odd	2		3330.2.d.p.1999.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.b.d.149.3	✓	10	1.1	even	1	trivial
370.2.b.d.149.8	yes	10	5.4	even	2	inner
1850.2.a.bd.1.3		5	5.3	odd	4
1850.2.a.be.1.3		5	5.2	odd	4
3330.2.d.p.1999.4		10	15.14	odd	2
3330.2.d.p.1999.9		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -0.332924i q^{3} -1.00000 q^{4} +(-1.10390 + 1.94458i) q^{5} -0.332924 q^{6} -3.51336i q^{7} +1.00000i q^{8} +2.88916 q^{9} +(1.94458 + 1.10390i) q^{10} -0.290044 q^{11} +0.332924i q^{12} -7.12558i q^{13} -3.51336 q^{14} +(0.647398 + 0.367517i) q^{15} +1.00000 q^{16} -6.17921i q^{17} -2.88916i q^{18} -5.83553 q^{19} +(1.10390 - 1.94458i) q^{20} -1.16968 q^{21} +0.290044i q^{22} +6.45973i q^{23} +0.332924 q^{24} +(-2.56279 - 4.29326i) q^{25} -7.12558 q^{26} -1.96065i q^{27} +3.51336i q^{28} +1.18043 q^{29} +(0.367517 - 0.647398i) q^{30} +9.77838 q^{31} -1.00000i q^{32} +0.0965628i q^{33} -6.17921 q^{34} +(6.83201 + 3.87841i) q^{35} -2.88916 q^{36} -1.00000i q^{37} +5.83553i q^{38} -2.37228 q^{39} +(-1.94458 - 1.10390i) q^{40} +1.64077 q^{41} +1.16968i q^{42} +5.34889i q^{43} +0.290044 q^{44} +(-3.18936 + 5.61821i) q^{45} +6.45973 q^{46} +5.69256i q^{47} -0.332924i q^{48} -5.34367 q^{49} +(-4.29326 + 2.56279i) q^{50} -2.05721 q^{51} +7.12558i q^{52} -9.32034i q^{53} -1.96065 q^{54} +(0.320181 - 0.564014i) q^{55} +3.51336 q^{56} +1.94279i q^{57} -1.18043i q^{58} -5.94279 q^{59} +(-0.647398 - 0.367517i) q^{60} -1.27699 q^{61} -9.77838i q^{62} -10.1507i q^{63} -1.00000 q^{64} +(13.8563 + 7.86596i) q^{65} +0.0965628 q^{66} +6.04334i q^{67} +6.17921i q^{68} +2.15060 q^{69} +(3.87841 - 6.83201i) q^{70} +13.4995 q^{71} +2.88916i q^{72} -1.71348i q^{73} -1.00000 q^{74} +(-1.42933 + 0.853215i) q^{75} +5.83553 q^{76} +1.01903i q^{77} +2.37228i q^{78} -8.25422 q^{79} +(-1.10390 + 1.94458i) q^{80} +8.01474 q^{81} -1.64077i q^{82} -2.41807i q^{83} +1.16968 q^{84} +(12.0160 + 6.82126i) q^{85} +5.34889 q^{86} -0.392995i q^{87} -0.290044i q^{88} +10.2797 q^{89} +(5.61821 + 3.18936i) q^{90} -25.0347 q^{91} -6.45973i q^{92} -3.25546i q^{93} +5.69256 q^{94} +(6.44187 - 11.3477i) q^{95} -0.332924 q^{96} +15.1272i q^{97} +5.34367i q^{98} -0.837984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{4} + 6 q^{5} - 6 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{14} + 10 q^{16} - 8 q^{19} - 6 q^{20} + 32 q^{21} + 4 q^{25} - 12 q^{26} - 22 q^{29} + 20 q^{30} + 46 q^{31} - 18 q^{34} + 32 q^{35} + 6 q^{36}+ \cdots + 22 q^{99}+O(q^{100}) \) 10 * q - 10 * q^4 + 6 * q^5 - 6 * q^9 + 2 * q^10 + 6 * q^11 + 2 * q^14 + 10 * q^16 - 8 * q^19 - 6 * q^20 + 32 * q^21 + 4 * q^25 - 12 * q^26 - 22 * q^29 + 20 * q^30 + 46 * q^31 - 18 * q^34 + 32 * q^35 + 6 * q^36 - 40 * q^39 - 2 * q^40 - 14 * q^41 - 6 * q^44 + 2 * q^45 + 12 * q^46 - 60 * q^49 + 8 * q^50 - 40 * q^51 + 42 * q^55 - 2 * q^56 - 40 * q^59 - 18 * q^61 - 10 * q^64 + 4 * q^65 + 40 * q^66 - 32 * q^69 - 6 * q^70 + 12 * q^71 - 10 * q^74 + 50 * q^75 + 8 * q^76 - 40 * q^79 + 6 * q^80 - 14 * q^81 - 32 * q^84 + 36 * q^85 - 34 * q^86 - 24 * q^89 + 44 * q^90 + 32 * q^91 - 24 * q^94 + 12 * q^95 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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